Search Results (251)

This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing stochastic demand dynamics. The production and inventory cost optimization problem is formulated as a quadratic cost functional, with the solution characterized by a regime-dependent system of elliptic partial differential equations (PDEs). Numerical solutions to the PDE system are computed using a monotone iteration algorithm, enabling quantitative analysis. Sensitivity analysis and model risk evaluation illustrate the effects of regime-dependent volatility, holding costs, and discount factors, revealing the conservative bias of regime-switching models when compared to static alternatives. Practical implications include optimizing production strategies under fluctuating economic conditions and exploring future extensions such as correlated Brownian dynamics, non-quadratic cost functions, and geometric inventory frameworks. In contrast to earlier studies that imposed static or overly simplified regime-switching assumptions, our work presents a fully integrated framework—combining optimal control theory, a regime-dependent system of elliptic PDEs, and comprehensive numerical and sensitivity analyses—to more accurately capture the complex stochastic dynamics of production planning and thereby deliver enhanced, actionable insights for modern manufacturing environments. Full article

Combining Brownian dynamics simulations and self-consistent field theory, we demonstrate that stable assembled structures, such as vesicles, toroidal micelles, bowl-like micelles, sheet-like micelles, non-spherical vesicles, and cylindrical micelles, are dependent on the molecular parameters of amphiphilic comb-like copolymers. Importantly, we find that vesicle formation involves two intermediate states, sheet-like and bowl-like micelles, and the difference in their free energies is minimal, which illustrates the coexisting phase between them. Moreover, the assembled vesicles can be modulated in the membrane thickness with overall size, unchanged only by adjusting the backbone length. We also demonstrate the coexistence of toroidal and cylindrical micelles because neither structure has a significant advantage over the other in free energy. Our work points out how to obtain different morphologies by adjusting the molecular parameters of amphiphilic comb-like copolymers, instilling confidence in their potential for stable drug encapsulation and enhanced targeted drug delivery. Full article

We investigate the bridge problem for stochastic processes, that is, we analyze the statistical properties of trajectories constrained to begin and terminate at a fixed position within a time interval $\tau$. Our primary focus is the time-reversal symmetry of these trajectories: under which conditions do the statistical properties remain invariant under the transformation $t\to \tau -t$? To address this question, we compare the stochastic differential equation describing the bridge, derived equivalently via Doob’s transform or stochastic optimal control, with the corresponding equation for the time-reversed bridge. We aim to provide a concise overview of these well-established derivation techniques and subsequently obtain a local condition for the time-reversal asymmetry that is specifically valid for the bridge. We are specifically interested in cases in which detailed balance is not satisfied and aim to eventually quantify the bridge asymmetry and understand how to use it to derive useful information about the underlying out-of-equilibrium dynamics. To this end, we derived a necessary condition for time-reversal symmetry, expressed in terms of the current velocity of the original stochastic process and a quantity linked to detailed balance. As expected, this formulation demonstrates that the bridge is symmetric when detailed balance holds, a sufficient condition that was already known. However, it also suggests that a bridge can exhibit symmetry even when the underlying process violates detailed balance. While we did not identify a specific instance of complete symmetry under broken detailed balance, we present an example of partial symmetry. In this case, some, but not all, components of the bridge display time-reversal symmetry. This example is drawn from a minimal non-equilibrium model, namely Brownian Gyrators, that are linear stochastic processes. We examined non-equilibrium systems driven by a "mechanical” force, specifically those in which the linear drift cannot be expressed as the gradient of a potential. While Gaussian processes like Brownian Gyrators offer valuable insights, it is known that they can be overly simplistic, even in their time-reversal properties. Therefore, we transformed the model into polar coordinates, obtaining a non-Gaussian process representing the squared modulus of the original process. Despite this increased complexity and the violation of detailed balance in the full process, we demonstrate through exact calculations that the bridge of the squared modulus in the isotropic case, constrained to start and end at the origin, exhibits perfect time-reversal symmetry. Full article

Parabolic trough collector (PTC) systems, often deployed in arid regions, are vulnerable to dust accumulation (soiling), which reduces mirror reflectivity and energy output. This study presents a physically based soiling forecast algorithm (SFA) designed to estimate soiling levels. The model was calibrated and validated using three meteorological data sources—numerical forecasts (YR), METAR observations, and on-site measurements—from a PTC facility in Limassol, Cyprus. Field campaigns covered dry, rainy, and red-rain conditions. The model demonstrated robust performance, particularly under dry summer conditions, with normalized root mean square errors (NRMSE) below 1%. Sedimentation emerged as the dominant soiling mechanism, while the contributions of impaction and Brownian motion varied according to site-specific environmental conditions. Under dry deposition conditions, the reflectivity change rate during spring and autumn was approximately twice that of summer, indicating a need for more frequent cleaning during transitional seasons. A red-rain event resulted in a pronounced drop in reflectivity, showcasing the model’s ability to capture abrupt soiling dynamics associated with extreme weather episodes. The proposed SFA offers a practical, adaptable tool for reducing soiling-related losses and supporting seasonally adjusted maintenance strategies for solar thermal systems. Full article

We investigate a two-dimensional system of active Brownian dumbbells using molecular dynamics simulations. In this model, each dumbbell is driven by an active force oriented perpendicular to the axis connecting its two constituent beads. We characterize the resulting phase behavior and find that, across all values of activity, the system undergoes phase separation between dilute and dense phases. The dense phase exhibits hexatic order, and for large enough activity, we observe a marked increase in local polarization, with dumbbells predominantly oriented towards the interior of the clusters. Compared to the case of axially self-propelled dumbbells, we find that the binodal region is enlarged towards lower densities at all activities. This shift arises because dumbbells with transverse propulsion can more easily form stable cluster cores, serving as nucleation seeds, and show a highly suppressed escaping rate from the cluster boundary. Finally, we observe that clusters exhibit spontaneous rotation, with the modulus of the angular velocity scaling as $\omega \sim r_g^{-2}$, where $r_g$ is the cluster’s radius of gyration. This contrasts with axially propelled dumbbells, where the scaling follows $\omega \sim r_g^{-1}$. We develop a simplified analytical model to rationalize this scaling behavior. Full article

The scaling up of carbon capture, utilization, and storage (CCUS) deployment is constrained by multiple factors, including technological immaturity, high capital expenditures, and extended investment return periods. The existing research on CCUS investment decisions predominantly centers on coal-fired power plants, with the utilization pathways placing a primary emphasis on storage or enhanced oil recovery (EOR). There is limited research available regarding the chemical utilization of carbon dioxide (CO₂). This study develops an options-based analytical model, employing geometric Brownian motion to characterize carbon and oil price uncertainties while incorporating the learning curve effect in carbon capture infrastructure costs. Additionally, revenues from chemical utilization and EOR are integrated into the return model. A case study is conducted on a process producing 100,000 tons of methanol annually via CO₂ hydrogenation. Based on numerical simulations, we determine the optimal investment conditions for the “CO₂-to-methanol + EOR” collaborative scheme. Parameter sensitivity analyses further evaluate how key variables—carbon pricing, oil market dynamics, targeted subsidies, and the cost of renewable electricity—influence investment timing and feasibility. The results reveal that the following: (1) Carbon pricing plays a pivotal role in influencing investment decisions related to CCUS. A stable and sufficiently high carbon price improves the economic feasibility of CCUS projects. When the initial carbon price reaches 125 CNY/t or higher, refining–chemical integrated plants are incentivized to make immediate investments. (2) Increases in oil prices also encourage CCUS investment decisions by refining–chemical integrated plants, but the effect is weaker than that of carbon prices. The model reveals that when oil prices exceed USD 134 per barrel, the investment trigger is activated, leading to earlier project implementation. (3) EOR subsidy and the initial equipment investment subsidy can promote investment and bring forward the expected exercise time of the option. Immediate investment conditions will be triggered when EOR subsidy reaches CNY 75 per barrel or more, or the subsidy coefficient reaches 0.2 or higher. (4) The levelized cost of electricity (LCOE) from photovoltaic sources is identified as a key determinant of hydrogen production economics. A sustained decline in LCOE—from CNY 0.30/kWh to 0.22/kWh, and further to 0.12/kWh or below—significantly advances the optimal investment window. When LCOE reaches CNY 0.12/kWh, the project achieves economic viability, enabling investment potentially as early as 2025. This study provides guidance and reference cases for CCUS investment decisions integrating EOR and chemical utilization in China’s refining–chemical integrated plants. Full article

Sometimes, limits can be singular, implying that they take on different values depending on the order of arithmetic operations. In other words, the limit map lacks commutativity. While all such limits are mathematically valid, only one can be the physical limit. The change of measure for Brownian processes illustrates this phenomenon. A substantial body of elegant mathematics centered around continuous-time Brownian processes has been embraced by the physics community to investigate the nonequilibrium and equilibrium thermodynamics of systems composed of atoms and molecules. In this paper, we derive the continuous-time limit of discrete-time Brownian dynamics, specifically focusing on the change of measure. We demonstrate that this result yields the physical limit that differs from the commonly used expression. Consequently, the concepts of “the most probable path”, “minimum thermodynamic action”, and “the small-noise limit” are unphysical mathematical artifacts. Full article

This study examines the price dynamics of the UK Emission Trading Scheme (UK ETS) by integrating advanced computational methods, including deep learning and statistical modelling, to analyze and simulate carbon market behaviour. By analyzing long-memory effects and price volatility, it assesses whether UK carbon prices align with theoretical expectations from carbon pricing mechanisms and market efficiency theories. Findings indicate that UK carbon prices exhibit persistent long-memory effects, contradicting the Efficient Market Hypothesis, which assumes price movements are random and fully reflect available information. Furthermore, regulatory interventions exert significant downward pressure on prices, suggesting that policy uncertainty disrupts price equilibrium in cap-and-trade markets. Deep learning models, such as Time-series Generative Adversarial Networks (TGANs) and adjusted fractional Brownian motion, outperform traditional approaches in capturing price dependencies but are prone to overfitting, highlighting trade-offs in AI-based forecasting for carbon markets. These results underscore the need for predictable regulatory frameworks, hybrid pricing mechanisms, and data-driven approaches to enhance market efficiency. By integrating empirical findings with economic theory, this study contributes to the carbon finance literature and provides insights for policymakers on improving the stability and effectiveness of emissions trading systems. Full article

This paper introduces a novel numerical approach for solving fractional stochastic differential equations (FSDEs) using bilinear time-series models, driven by the Caputo–Katugampola (C-K) fractional derivative. The C-K operator generalizes classical fractional derivatives by incorporating an additional parameter, enabling the enhanced modeling of memory effects and hereditary properties in stochastic systems. The primary contribution of this work is the development of an efficient numerical framework that combines bilinear time-series discretization with the C-K derivative to approximate solutions for FSDEs, which are otherwise analytically intractable due to their nonlinear and memory-dependent nature. We rigorously analyze the impact of fractional-order dynamics on system behavior. The bilinear time-series framework provides a computationally efficient alternative to traditional methods, leveraging multiplicative interactions between past observations and stochastic innovations to model complex dependencies. A key advantage of our approach is its flexibility in handling both stochasticity and fractional-order effects, making it suitable for applications in a famous nuclear physics model. To validate the method, we conduct a comparative analysis between exact solutions and numerical approximations, evaluating convergence properties under varying fractional orders and discretization steps. Our results demonstrate robust convergence, with simulations highlighting the superior accuracy of the C-K operator over classical fractional derivatives in preserving system dynamics. Additionally, we provide theoretical insights into the stability and error bounds of the discretization scheme. Using the changes in the number of simulations and the operator parameters of Caputo–Katugampola, we can extract some properties of the stochastic fractional differential model, and also note the influence of Brownian motion and its formulation on the model, the main idea posed in our contribution based on constructing the fractional solution of a proposed fractional model using known bilinear time series illustrated by application in nuclear physics models. Full article

A model is proposed to investigate the effects of power generation source diversification and CO₂ emission control in the presence of dispatchable fossil fuel sources and non-dispatchable carbon-free renewables. In a stochastic environment in which three random factors are considered, namely fossil fuels (gas and coal) and CO₂ prices, we discuss a planning methodology for power system portfolio selection that integrates the non-dispatchable renewables available in a given energy system and optimally combines cost, risk and CO₂ emissions. By combining the deep neural network probabilistic forecasting of fossil fuel path prices with a geometric Brownian motion model for describing the CO₂ price dynamics, we simulate a wide range of plausible market scenarios. Results show that under CO₂ price volatility, optimal portfolios shift toward cleaner energy sources, even in the absence of explicit emission targets, highlighting the implicit regulatory power of volatility. The results suggest that incorporating CO₂ price volatility through market mechanisms can serve as an effective policy tool for driving decarbonization. Our model offers a flexible and reproducible approach to support policy design in energy planning under uncertainty. Full article

The use of perovskite manganite nanoparticles in magnetic hyperthermia has attracted significant attention due to their tunable magnetic properties and high specific absorption rate (SAR). In this work, we present a combined experimental and theoretical investigation of the frequency- and amplitude-dependent magnetic heating behavior of La_0.51Sr_0.49MnO₃ (LSMO) and Dy-doped La_0.51Dy_0.045Sr_0.445MnO₃ (DLSMO) nanoparticles. The nanoparticles were synthesized via the sol–gel method and characterized by XRD and SEM, while SAR values were experimentally evaluated under varying magnetic field strengths (60–120 Oe) and frequencies (150–300 kHz). In parallel, theoretical modeling based on Néel and Brownian relaxation mechanisms was employed to predict SAR behavior as a function of particle size, magnetic anisotropy, and fluid viscosity. The results reveal that Dy doping enhances magnetic anisotropy, which modifies the relaxation dynamics and leads to a reduction in SAR. The model identifies the optimal nanoparticle size (~18–20 nm) and ferrofluid viscosity to maximize heating efficiency. This combined approach provides a comprehensive framework for designing and optimizing perovskite-based nanoparticles for magnetic hyperthermia applications. Full article

In order to realize green and low-carbon transformation, some ports have explored the path of sustainable equipment upgrading by adjusting the energy structure of yard cranes in recent years. However, there are multiple uncertainties in the investment process of hydrogen-powered yard cranes, and the existing valuation methods fail to effectively deal with these dynamic changes and lack scientifically sound decision support tools. To address this problem, this study constructs a multi-factor real options model that integrates the dynamic uncertainties of hydrogen price, carbon price, and technology maturity. In this study, a geometric Brownian motion is used for hydrogen price simulation, a Markov chain model with jump diffusion term and stochastic volatility is used for carbon price simulation, and a learning curve method is used to quantify the evolution of technology maturity. Aiming at the long investment cycle of ports, a hybrid option strategy of “American and European” is designed, and the timing and scale of investment are dynamically optimized by Monte Carlo simulation and least squares regression. Based on the empirical analysis of Qingdao Port, the results show that the optimal investment plan for hydrogen-powered yard cranes project under the framework of a multi-factor option model is to use an American-type option to maintain moderate flexibility in the early stage, and to use a European-type option to lock in the return in the later stage. The study provides decision support for the green development of ports and enhances economic returns and carbon emission reduction benefits. Full article

In this study, we present a novel mathematical framework for pricing financial derivates and modelling asset behaviour by bringing together fractional Brownian motion (fBm), fuzzy logic, and jump processes, all aligned with no-arbitrage principle. In particular, our mathematical developments include fBm defined through Mandelbrot-Van Ness kernels, and advanced mathematical tools such Molchan martingale and BDG inequalities ensuring rigorous theoretical validity. We bring together these different concepts to model uncertainties like sudden market shocks and investor sentiment, providing a fresh perspective in financial mathematics and derivatives pricing. By using fuzzy logic, we incorporate subject factors such as market optimism or pessimism, adjusting volatility dynamically according to the current market environment. Fractal mathematics with the Hurst exponent close to zero reflecting rough market conditions and fuzzy set theory are combined with jumps, representing sudden market changes to capture more realistic asset price movements. We also bridge the gap between complex stochastic equations and solvable differential equations using tools like Feynman-Kac approach and Girsanov transformation. We present simulations illustrating plausible scenarios ranging from pessimistic to optimistic to demonstrate how this model can behave in practice, highlighting potential advantages over classical models like the Merton jump diffusion and Black-Scholes. Overall, our proposed model represents an advancement in mathematical finance by integrating fractional stochastic processes with fuzzy set theory, thus revealing new perspectives on derivative pricing and risk-free valuation in uncertain environments. Full article

Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental science over several decades. Time series of water and matter fluxes and nutrient concentrations from these systems exhibit a bewildering diversity of spatiotemporal patterns, indicating the intricate nature of processes acting on a large range of time scales. Nonlinear dynamics is an obvious framework to investigate catchment time series. We analyzed selected long-term data from three headwater catchments in the Bramke valley, Harz mountains, Lower Saxony in Germany at common biweekly resolution for the period 1991 to 2023. For every time series, we performed gap filling, detrending, and removal of the annual cycle using singular system analysis (SSA), and then calculated metrics based on ordinal pattern statistics: the permutation entropy, permutation complexity, and Fisher information, as well as their generalized versions (q-entropy and α-entropy). Further, the position of each variable in Tarnopolski diagrams is displayed and compared to reference stochastic processes, like fractional Brownian motion, fractional Gaussian noise, and β noise. Still another way of distinguishing deterministic chaos and structured noise, and quantifying the latter, is provided by the complexity from ordinal pattern positioned slopes (COPPS). We also constructed horizontal visibility graphs and estimated the exponent of the decay of the degree distribution. Taken together, the analyses create a characterization of the dynamics of these systems which can be scrutinized for universality, either across variables or between the three geographically very close catchments. Full article

The rate of nucleation of crystals is the subject of extensive research, since it—together with the nucleation time—determines the number of crystals growing; in turn, their number is related to their size. Experimental studies show that, for biomolecular crystals, despite the required unusually high supersaturations, the nucleation process is distinctly slow. This slowness arises from the inherent peculiarity of the nucleation of such crystals. Therefore, a prerequisite for management of the crystallization process towards the desired outcome is the molecular level understanding of the nucleation mechanism. In this paper, analyzing the mechanisms behind the nucleation process of protein crystals, it is argued that the highly inhomogeneous molecule surface is the main reason for the slow crystal nucleation: only a few small patches on their surface are capable of forming crystalline bonds. Therefore, the partner proteins must not only be brought to encounter one another but must also find each other’s binding site. In turn, this requirement imposes a severe steric restriction on the association of protein molecules, which, however, is alleviated by a rotational-diffusional reorientation. This is why particular attention is paid to this aspect of the protein crystal nucleation process. Full article